Oxidation state dependence of the geometry, electronic structure, and magnetic coupling in mixed oxo- and carboxylato-bridged manganese, dimers

Approximate density functional theory has been used to investigate changes in the geometry and electronic structure of the mixed oxo- and carboxylato-bridged dimers [Mn₂(μ-O)₂(O₂CH) (NH₃)₆]ⁿ⁺ and [Mn₂(μ-O)(O₂CH)₂ (NH₃)₆]ⁿ⁺ in the Mn^IVMn^IV, Mn^IIIMn^IV, and Mn^IIIMn^III oxidation states. The magnetic coupling in the dimer is profoundly affected by changes in both the bridging ligands and Mn oxidation state. In particular, change in the bridging structure has a dramatic effect on the nature of the Jahn-Teller distortion observed for the Mn^III centers in the III/III and III/IV dimers. The principal magnetic interactions in [Mn₂(μ-O)₂(O₂CH) (NH₃)₆]ⁿ⁺ involve the J_xz/xz and J_yz/yz pathways but due to the tilt of the Mn₂O₂ core, they are less efficient than in the planar di-μ-oxo structure and, consequently, the calculated exchange coupling constants are generally smaller. In both the III/III and III/IV dimers, the Mn^III centers are high-spin, and the Jahn-Teller effect gives rise to axially elongated Mn^III geometries with the distortion axis along the Mn-O_c bonds. In the III/IV dimer, the tilt of the Mn₂O₂ core enhances the crossed exchange J_x²-_y²/_z² pathway relative to the planar di-μ-oxo counterpart, leading to significant delocalization of the odd electron. Since this delocalization pathway partially converts the Mn^IV ion into low-spin Mn^III, the magnetic exchange in the ground state can be considered to arise from two interacting spin ladders, one is the result of coupling between Mn^IV (S = 3/2) and high-spin Mn^III (S = 2), the other is the result of coupling between Mn^IV (S = 3/2) and low-spin Mn^III (S = 1). In [Mn₂(μ-O)(O₂CH)₂ (NH₃)₆]ⁿ⁺, both the III/III dimer and the lowest energy structure for the III/IV dimer involve high-spin Mn^III, but the Jahn-Teller axis is now orientated along the Mn-oxo bond, giving rise to axially compressed Mn^III geometries with long Mn-O_c equatorial bonds. In the IV/IV dimer, the ferromagnetic crossed exchange J_yz/z² pathway partially cancels J_yz/yz and, as a consequence, the antiferromagnetic J_xz/xz pathway dominates the magnetic coupling. In the III/III dimer, the J_yz/yz pathway is minimized due to the smaller Mn-O-Mn angle, and since the ferromagnetic J_yz/z² pathway largely negates J_xz/xz, relatively weak overall antiferromagnetic coupling results. In the III/IV dimer, the structures involving high-spin and low-spin Mn^III are almost degenerate. In the high-spin case, the odd electron is localized on the Mn^III center, and the resulting antiferromagnetic coupling is similar to that found for the IV/IV dimer. In the alternative low-spin structure, the odd electron is significantly delocalized due to the crossed J_yz/z² pathway, and cancellation between ferromagnetic and antiferromagnetic pathways leads to overall weak magnetic coupling. The delocalization partially converts the Mn^IV ion into high-spin Mn^III, and consequently, the spin ladders arising from coupling of Mn^IV (S = 3/2) with high-spin (S = 2) and low-spin (S = 1) Mn^III are configurationally mixed. Thus, in principle, the ground-state magnetic coupling in the mixed-valence dimer will involve contributions from three spin-ladders, two associated with the delocalized low-spin structure and the third arising from the localized high-spin structure.